KöMaL 2014 C1207

$E$, $F$ and $G$ are points on each side of triangle ABC and $n$ is a natural number such that $\frac{AE}{EB}=\frac{1}{n-1}$, $\frac{BF}{FC}=\frac{1}{n}$ , and $\frac{CG}{GA}=\frac{1}{n+1}$. Show that if $n \ge$5 then the area of triangle EFG is greater than the half of the area of triangle ABC .